Thermal properties calculated from measured water content as a function of depth in porcine skin

556

Burns (1986) 12, (8). 556562

Printedin Great Britain

Thermal properties calculated from measured water content as a function of depth in porcine skin F. S. Knox III Crew Biotechnology, Alabama, USA

US Army Aeromedical

Research Laboratory,

Fort Rucker,

T. L. Wachtel Trauma and Burn Service, Good Samaritan

Medical Center, Phoenix, Arizona, USA

G. R. McCahan Department of Toxicology and Criminal Investigation, Alabama, USA

State ofAlabama,

Enterprise,

and S. C. Knapp US Central Command,

MacDill Air Force Base, Tampa, Florida, USA

Summary In order to develop a realistic tissue water boiling routine for a mathematical model of burn development, it was necessary to know the water content and the thermal properties of skin as a function of depth. Split thickness skin samples were obtained from several pigs using an air-powertd dermatome. Alternate segments of these skin slices were processed for skin water content determination and for histopathologic measurements of skin thickness. Tissue samples were weighed, dried and subsequently weighed again using standardized methods to determine tissue water content. In some instances the volume of tissue was also determined to allow the calculation of tissue density. Given a table of measured values of water content as a function of skin thickness, a least-squares cubic polynomial was fitted to the data and water content as a function of depth was computed from the following formula: w(T-d)=T/dx(WT-WT__J+WT_,, where T is the total thickness of a skin slice, W,is the fraction of water computed from the cubic equation, d is the thickness of the skin slice at a depth T-d, and WTmd is the fraction of water above the thin slice. Stratum

corneum hydration was calculated from measured ambient relative humidity based on a relationship previously described by Rushmer et al. (1966). Skin thermal properties as a function of depth were calculated using the formulation of Cooper and Trezek (1971). Computer simulations incorporating these new thermal properties and the water profile into our previously presented model (Knox et al., 1978 a) show that these changes have resulted in improved predicted burn depths as judged by reduced root mean square (r.m.s.) error. Using this method studies can now be made of the changes in thermal properties which occur during various stages of thermal tissue damage, e.g. oedema, protein coagulation and shrinkage due to desiccation.

INTRODUCTION porcine skin is subjected to a simulated post-crash fire as in the US Army Aeromedical Research Laboratory (USAARL) bioassay technique, the tissue water boils and steam blebs are formed (Knox et al., 1973). Any model that WHEN

557

Knox et al.: Calculations of thermal properties predicts burn depths accurately must account for the energy lost in this process of vaporization and an algorithm that models tissue water boiling requires the knowledge of tissue water content as a function of depth. Likewise, the calculation of heat flow through the skin in such a model requires that the conductivity (K), heat capacity (Cp), and density (y) be known as a function of depth. Gillman (lY70) citing Giinter Stiittgen reports that skin water increases from a low of 2 per cent in stratum corneum to a high of 71 per cent in the stratum papillaris before falling to 30 per cent in the subcutaneous fat. Eisele and Eichelberger (1945) found freshly excised human skin without fat to contain 69 to 74 per cent water with a mean of 71.8 per cent. No mention is made of the ambient conditions under which these data were derived. When epidermis is separated from dermis in fat-free human skin by placing the dermis on a hot plate at 50°C for 2 min and peeling off the epidermis, its water content was found by Zheutlin and Fox (1950) to average 66.12k2.61 per cent for breast and 61.2k1.56 per cent for leg. Walser and Bodenlos (1954). in studying water and electrolytes in rat skin following experimental flash burns. found tissue water ranging from 65+4 to 82+3g/lOOg with no orderly progression in relation to the burn. They observed most of the oedema to be subcutaneous. Based on an earlier review showing the pig as an established model for the study of burn problems (Montagna. IYhh; Weinstein, IYhh; Knox et al.. lY7Xb. lY7Y) and on the fairly narrow range of tissue water in general. it can be assumed that the water content of porcine skin would be reasonably close to the values quoted above for human skin. Nonetheless, there appears to be no good data. either pig or human, relating water content to depth with the precision required by a model. Thus, the experimental determination of tissue water content is a requisite to further burn model development. In IYhO. Spells reported a correlation between tissue water content and thermal conductivity. Subsequently. other investigators (Poppendiek et al.. 1966) added the concept that as far as thermal conductivity was concerned, all tissues were composed of water, protein and fat and that the lumped conductivity was a weighted sum of the individual conductivities of the constituents using a parallel heat Row model. Cooper and Trezek (lY71) expanded upon these earlier ideas and showed that, “Tissue thermal conductivity, density and specific heat can, in general, be pre-

Fig. 1. Anaesthetized thickness

skin

pig showing

locations

of split

slabs

removed from the lateral aspect with an air-powered dermatome.

dieted to within an accuracy of 5 per cent [using their equations) and the assumption that tissue is composed of water and of protein and fat in equal proportions.” In this paper we will follow Cooper and Trezek’s lead and use the measured skin water to calculate the conductivity. density and heat capacity as a function of depth. METHODS Eighty-two split thickness or full thickness skin samples were obtained from the lateral aspect of six anaesthetized domestic white pigs (Sus scrofu) using an air-powered dermatome (Fig. 1). The long narrow skin grafts of various thicknesses were cut transversely into segments (or slabs) and alternate segments were processed to determine either water content or skin thickness. The histopathologic measurements of skin thickness followed the protocol described by Knox et al. (1978 a). Tissue samples for water content determination were handled as follows: (1) each sample was assigned a tissue number and placed in an Armed Forces Institute of Pathology (AFIP) bag; (2) weighing trays marked with the sample number were heated in an oven at 180°C for 1h: (3) the trays were held in a desiccator for I h; (4) trays were weighed giving a dry tare weight; (5) tissue samples were removed from the envelopes. blotted, placed on the trays and weighed; (6) samples were then placed in an oven at 106” C for 35 h under a 30in (76cm) mercury vacuum; (7) samples were then placed on a desiccator for 4 h: (8) samples were weighed, giving dry weight no. l=unbound water: (9) samples were then placed again in an oven at 147” C for 50 h under a 30 in (76 cm) mercury vacuum; (10) samples were put in a desiccator for 36 h and subsequently weighed again to determine the dry weight no. 2=bound water. The percentage of water was calculated on the basis of the ratio of dry weight

558

Burns

no. 2 to the sample wet weight. The thickness of the skin was taken as the average thickness of the adjacent samples as measured from 8 urn sections under a microscope. In some instances, the tissue volume was measured by observing the amount of water displaced by a piece of skin placed in a graduated cylinder. Density was calculated from the measurement of tissue volume and weight. Water content vs. thickness data were fitted with a cubic polynomial using least-squares criteria, and water content as a function of depth was calculated from the cubic polynomial. (Program available on request.)

The calculations relating water content to skin thickness and the associated thermal properties of the tissues were computed from the formulas given in the Appendix.

The raw data of water content vs. skin thickness are shown in Fig. 2. These data were fitted with a cubic polynomial using least-squares techniques and the water content as a function of depth was then computed from this polynomial. The computed water content was then used to compute density, thermal conductivity and heat capacity as a function of depth. The results of these calculations are summarized in Table 1. The least reliable portion of this table is the portion from 80um to the surface since no valid data was collected for this region. Using the data provided by Rushmer et al. (1966) of the weight gain of desiccated stratum corneum vs. relative humidity and the humidity recorded during the pig experi-

Depth (pm) 10 200 400 600 800 1000 1200 1400 1600 1800 2000

70.55

k 3 2

66.04

Y %

61.52

57.00 .oo

55.00

110.00

165.00

220.00

SKIN DEPTH MICROMETERS

4 1.20 I ;

.90 I

’

30

E u

.30

a

3

.oo

,

40.00

30.00

120.00

160.00

DEPTH IN MICROMETERS

water by thickness, percentage water by depth, thermal density, and heat capacity for porcine skin, beginning at 10 urn and to a depth of 2100um

66.473 69.811 72.120 73.354 73.677 73.251 72.240 70.806 69.114 67.326 65.604

Water by depth (%I 66.473 72.596 75.574 75.638 73.439 69.632 64.869 59.800 55.081 51.364 49.298

200.00

I

240.00

x10’

Fig. 3. Values of water, conductivity and heat capacity xdensity versus depth as used in the model BRNSIM. Ambient relative humidity assumed to be 60 per cent. M-M, Water (g/cm’); O-0, conductivity (caUcmM”C); A-A, heat capacityxdensity (caVcm7/“C).

Percentage

Water by thickness (%I

2i 00

x10’

1.50 T

RESULTS

conductivity, every 200um

Vol. 12/No. 8

Fig. 2. Percentage water by weight vs. thickness of skin slab. (00) Circled data points contained some subcutaneous fat. These data were fitted with a cubic equation.

Calculations

Table 1.

B

(1986)

Thermal conductivity

Heat capacity

(cal/cm/sPC)

(g/cm$

(cal/g/T)

1.1605~10-~ 1.2236~10-~~ 1.2541 x 1O-3 1.2647~10 3 1.2322~10 ’ 1~1931x10-a 1.1439x10-3 1~0912x10-3 1~0419xlo-3 1~0028~10-~ 9.8099x 10 4

1.0212 I.0172 1 .0153 1 .0153 1.0167 1.0191 1.0222 1.0255 I.0286 1.0310 I.0324

0.8005 0.8369 0.8547 0.8550 0.8420 0.8193 0.7910 0.7608 0.7327 0.7106 0.6983

Knox et al.: Calculations of thermal properties

559

Table II. Percentage water at 10 pm calculated by Y- 1.071e 0.0425x;rL=O-975, H20, X=relative humidity

where ‘f=percentage

Thermal conductivity (K)

Density w

Heat capacity (C)

Densityx heat capacity YC

Depth

% H,O by depth

Assuming 10 20 30 40 50 60 70 80

40 per cent relative humidity 5.9 5.0929x10 4 1.0618 14.934 6.0968x10 4 I.0555 23.968 7.0890x10~4 1.0493 33.002 8.0696x10 4 1.0432 42.036 9.0388x10 4 1.0372 51.07 9.9969x10 ' I.0312 60.104 1~0944x10 3 1.0253 69.138 1~1880x10 3 I.0195

04401 0.4939 0.5476 0.6014 0.6551 0.7089 0.7626 0.8164

0.4673 0.5213 0.5746 0.6274 0.6795 0.7310 0.7819 0.8323

Assuming 10 20 30 40 50 60 70 80

60percent 13.7 21.62 29.539 37.459 45.379 53.299 61.218 69.138

relativehumidity 5.9604x10 4 1.0564 6.8322~10 4 1.0509 7.6950x10 4 I.0455 8.5492x10 4 1.0402 9.3946x10 4 1.0350 1.0232~10 3 1.0297 1.1060~10 3 1.0246 1~1880x10 3 1.0195

0.4865 0.5336 0.5808 0.6279 0.6750 0.7221 0.7692 0.8164

0.5139 0.5608 0.6072 0.6531 0.6986 0.7435 0.7881 0.8323

Assuming 10 20 30 40 50 60 70 80

90percen 49.0 51.877 54.754 57.631 60.507 63.384 66.261 69.138

t relativehum ridity 9.7783x10 ' 1.0326 1~0082x10 3 I.0307 1.0384~10 3 1.0288 1.0686x10 3 I.0269 1.0986x10 3 1.0250 1.1285~10 3 1.0232 1.1583~10 3 I.0213 1~1880x10 3 I.0195

0.6966 0.7137 0.7308 0.7479 O-7650 0.7821 0.7993 0.8164

0.7193 0.7356 0.7518 0.7680 0.7841 0.8002 0.8163 0.8323

Derived from data in Rushmer et al. (1966). Remaining interpolated between value at 10 pm and value at 80 fem.

ments, it was possible to calculate water content of the stratum corneum (i.e., skin surface) for three different relative humidities. This water content was then set equal to the water content at lOurn. A lineary interpolation was made to derive intermediate values from this value at the 10 urn depth to the value at the 80 urn depth. The subsequent calculations of thermal conductivity, density and heat capacity were conducted based on these surface water profiles. The resulting values are summarized in Table II. The thermal properties of porcine skin VS. depth which are used in the current version of the burn prediction model BRNSIM are shown in graphical form in Fig. 3.

DISCUSSION This report presents a method for collecting split thickness skin samples. ascertaining water content and from that water content as a function of

values linearly

thickness, calculating water content as a function of depth and the thermal properties as a function of depth. The values for thermal conductivity thus calculated agree reasonably well with those reported for skin (mostly human) in reviews (Chato, 1969; Bowman et al., 1975). For instance, the mean (+s.e.m.) thermal conductivity for various skin samples reported by Bowman et al. (1975) is 1.0981x10-‘f0.071367 and the 95 per cent confidence limits are 0.95317 to 1.2429~ lo- cal/(cm/s/“C). The calculated values range from 0.50929~ 1V3 at 10 urn to 1.2577~ 10P3 at 490 urn, with all values at depths greater than 8Oum between 0.0788 and 1.2577~10~’ For the most part, the calculated values are well within the 95 per cent confidence region. If the data for epidermis, as reported by Bowman et al. (1975), are averaged separately, the mean (epidermis) is 0~5.50~0~0632~ 1V3 which is in good agreement with the epidermal

560

values found in Table II. The fact that some calculated values are slightly outside the range reported in the literature is not surprising, since most literature values for skin are from humans collected at an unspecified temperature while the calculated values are for pig collected at an ambient temperature of approximately 29” C (84°F) and a relative humidity of 56 per cent. At this temperature the cutaneous blood vessels are probably dilated, thereby changing the water content of the tissue samples (Moont, 1979). In living skin (Lipkin and Hardy, 1954) thermal inertias (KpC) from 90 to over 400X 10-s ca12/cmJ/ s/C) were found with increased blood flow due to heating, and Buettner (1936) reported a thermal conductivity of 6.7~10~’ for ‘very warm’ living human skin. Thus, the ambient temperature and the state of skin circulation should be taken into account because of its profound effect on conductivity. There is less than 1 per cent error associated with assuming a density of water=l.OOg/cm” in the temperature range of this study (Halliday and 1978). On the other hand, the Resnick, epidermis is roughly 2 per cent fat and 98 per cent fat-free solids (mostly protein) and dermis is approximately 23 per cent fat and 77 per cent fat-free solids after removal of water (Gillman, 1970). The algorithm used in the paper assumed that fat and protein make up a 50150 mixture after water removal. Use of the proper fat/ protein ratio would improve the fit of the model to the data (Cooper and Trezek, 1971). The knowledge of the thermal properties of the skin is obviously necessary to calculate the heat flow through the skin during burning. But it is just as important in gaining an understanding of the hyperthermia and hypothermia experienced by burned patients during recovery. Dittmar et al. (1978) measured conductivity of burnt skin and found a conductivity for dry eschar which was two to three times lower than normal, sometimes reaching as low as 4.0X 10e4 cal/(cm/s/ “C). The decrease in conductivity was greatest in children with their normally greater tissue water. They postulated that the dry eschar contributed to the hyperthermia seen before excision and that the hypothermia, seen with exudative skin is due to a large increase in effective conductivity with the removal of the dry eschar and the increase in moisture available for convective cooling. Thermal physiology of the burn patient will obviously have to integrate other factors, such as, loss of peripheral temperature sensors, hypothalamic reset and changes in -metabolism driven by the response to stress.

Burns

(1986) Vol. 12/No. 8

As with conductivity, the measured density (mean=l.OOSS, 1 s.e.m.=0.0198, 95 per cent confidence limits=0.96511-l.O458g/cm”) compares favourably with the calculated density which ranged from 1.0618 at 10um (40 per cent humidity) to 1.0151 at 460um (see Table I). For all depths greater than 80um, the calculated values ranged from 1.0151 to 1.0325g/cm3, well within the 95 per cent confidence region. The method of calculating tissue thermal properties as a function of depth, knowing the concentration of water, fat and protein presented here, can profitably be applied to the problems associated with diagnostic thermography. Many investigators (Draper and Jones, 1969; Draper and Boag, 1971; Nilsson and Gustafsson, 1974; Gustafsson et al., 1975; Nilsson, 1975; Vermey, 1975) have shown an understanding of the heat flow within tissue complete with its complex pattern of heat sources/sinks (blood vessels and possible tumours) which is required for thermography to become a more useful diagnostic tool. For the present, the thermal properties derived in this study have been useful in developing a burn prediction model BRNSIM which predicts burn depths with less r.m.s. error than e,arlier versions (Knox et al., 1980). CONCLUSIONS Tissue water contents and thermal properties as a function of depth in porcine skin were determined by measuring the water content of skin samples of various thicknesses and then calculating their thermal properties based on a model which treats then as the sum of thermal properties of the mass fraction of the constituents (water, fat and protein). This method is well established and gave reliable results. The water content was greatest at a depth of 500 urn (7593 as was the thermal conductivity per cent), (1.2577~10~“) and the heat capacity (0.8568). The density was highest at the dermal fat border (2100 urn from the surface). These data are consistent with those in the literature for human skin. The tissue water content and thermal properties have been useful in improving the predictive capability of a burn wound simulation model. This model can accurately predict the depth of burn, given the initial skin temperature and the time history of heat flux impinging on the skin surface. Acknowledgements The authors wish to acknowledge the funding for this project from the US Army Medical Research and Development Command and the US Air

561

Knox et al.: Calculations of thermal properties

Life Support SPO at Wright-Patterson Air Force Base. The views, opinions and/or findings contained in this report are those of the authors and should not be construed as an official Department of the

Force

position, policy or decision, unless so designated by other official documentation. Army

Appendix Calculations Glvcn a table of measured values of water content as a function ol skin thickness, a least-squares cubic polynomral was littcd 1o the data and water content as a function ol depth was computed from the formula:

W(T-d)=$

(U’r-

WT.,,)+

WT-d

where T is the total thickness of the split thickness skin sample. W, IS the fraction of water computed from the cubic equation. d is the thickness of a thin slab at a depth T-d. and Wr ,, is the fraction of water above the thin \lab. Thermal properties of the tissue were computed from the following equations (C’ooper and Trezek. 1971):

w,

thermal

w,

y= -+-+i Y”’ Yf

densq:

w, -’ YP

1

(1)

k, Ww +V’/ yV

+ kpwp

Yf

-]

YP

(3)

where the hubscript M’, / .lnd ,) rcfcr to water, fat and protcln. respectively. u’,, IS the mass fraction. y,, the density. ’p,, the heat capacity. and k,, the thermal contluctlvlty of the reapectivc components. Values of rhc various terms used wcrc (Cooper and I‘rczck. 1071):

I p/cm

( p,, = I 4)Ocal/pml”(‘ X II -- 1,.5X 10

‘cal/cm/~/“<‘

’p, --I I.55calipmi”~

‘1, =O.XlSg/cm

k,-4..5XlO

‘c;1l/cm/s/“(‘

Fat and protein wcrc absumcd to hc present amount\ (Cooper and l’rczek. IY71) so that-

and the resultant

equatmn\

y=(6.18277 K=y(l.O8432x

Bowman H., Frederick E. G., Cravalho J. J. et al. (1975) Theory, measurement and application of thcrma1 properties of biomaterials. Ann. Rev. Biophy.$. Bioenx. 4, 43. Bucttncr K. ( lY36) .S/rcth/er?/hc,~rrpic,55, 333. Chato J. C. (1969) Heat transfer in hioengineering. In: Chao B. T. (ed.), Advanced Heut Trunsferr. Urbana: University of Illinois Press, pp. 3Y5-414. Cooper T. E. and Trezck G. J. (1971) Correlation of thermal properties of some human tissue with water content. Aerospace Med. 42, 24. Dittmar A., Marichy J., Dunand M. et al. (lY7X) Thermal conductivity of burnt skin. 5rh /n/ernrtriotud Congress on Burn Injuries. l&23 June (abstract). Draper J. W. and Boag J. W. (lY71) The calculation 01 skein temperature distributions in thermography. Phvs. Med. Rio/. 16. 201. Draper J. W. and Jones C. H. (1969) Thermal patterns of the female breast. BY. J. Rudiol. 42. 401. Eisele C. W. and Eichelberger L. (1’145) Water. elcctrolyte and nitrogen content of human skin. Proc. Sot. Exp. Biol. Med. 58, 97. Gillman T. (1970) The dermis. In: Champion R. H.. Gillman T.. Rook A. J. et al. (eds). An Introduction IOthe Biology of the Skin. Philadelphia: F. A. Davis. chap. 6. Gustafsson S. E., Nilsson S. K. and Torrell L. N. (lY75) Analytical calculation of the skin temperature distribution due to subcutaneous heat production in a spherical heat source. Phys. Med. Biol. 20, 219. Halliday D. and Resnick R. (1978) Physics, Parts II, 3rd ed. New York: John Wiley, p. 47X.

conductivity:

K=y

I’,, =

REFERENCES

in equal

x 10 W,. +0.938172)-’

C’,,=O.YJ5

w

L!

15684x +0405.

and

Knox F. S. III, McCahan R. and Wachtel T. 1.. (lY73) The use of the pig as a bioassay substrate for evaluation of thermal protective clothing and physical scnsor calibration. Presented at the American Burn Association 5th Annual Meeting. Dallas. TX. (16 mm color sound film, 20 min.) Knox F. S. III, Wachtel T. L., Trevethan W. P. et al. (lY7Xa) A porcine bioassay method for analysis ol thermally protective fabrics: A histopathological and burn depth grading system. US Army Aeromedical Rcscarch Laboratory. Ft Rucker. Alabama. USAARL Report No. 7X-l I, June. Knox F. S. III, Wachtel T. L. and Knapp S. C‘. (lY7X h) How to measure the burn-preventive caoahilitv . , 01 non-flammable textiles: a comparison of the USAARL porcine bioassay technique with mathcmatical models. Bums 5. 19. Knox F. S., Wachtel T. 1~. and McCahan G. R. (lY70) Bioassav of thermal protection afforded hv candidate

Knox F. S.. Wachtel T. L. and Knapp S. C. (IWO) Burn prediction model for thermally protective clothing evaluation. Annual Meeting of the Acrospacc Medical Association, 12-15 May, Anaheim. CA.

wcrc:

10 W,,.+4

I

IO-~)

Lipkin M. and Hardy J. D. (IYS4) Measurement of some thermal orooerties of human tissues. J. .41,p/. Physiol. 7. 212’. ’

562

Burns (1986) Vol. 12/No. 8

Montagna W. (1966) The microscopic anatomy of the skin of swine and man. In: Bustad L. K., McClellen R. D. and Burns M. P. (eds), Swine in Biomedical Research. Seattle: Frayn Printing Co., p. 285. Moont L. E. (1979) Adaptation to Thermal Environment: Man and His Productive Animals. Baltimore: University Park, pp. 182-207. Nilsson S. K. (1975) Skin temperature over an artificial heat source implanted in man. Phys. Med. Biol. 20, 366. Nilsson S. K. and Gustafsson S. E. (1974) Surface temperature over an implant artificial heat source. Phys. Med. Biol. 19, 677. Poppendiek H. F., Randall R., Breeden J. A. et al. (1966) Thermal conductivity measurements and predictions for biological fluids and tissues. Cryobiology 3, 318. Rushmer R. F., Buettnew K. J. K., Short J. M. et al. (1966) The skin. Science 154. 343.

AMERICAN

Spells K. E. (1960) The thermal conductivity of some biological fluids. Phys. Med. Biol. 5, 139. Vermey G. F. (1975) The simulation of skin temperature distributions by means of a relaxation method. Phys. Med. Biol. 20, 384. Walser M. and Bodenlos L. J. (1954) Transfers of water and electrolytes between skin and extracellular fluid following extensive experimental flash burns. J. Appl. Physiol. 7, 19. Weinstein G. D. (1966) Comparison of turnover time and keratinous protein fractions in swine and human epidermis. In: Bustad L. K., McClellan R. D. and Burns M. P. (eds), Swine in Biomedical Research. Seattle: Frayn Printing Co., p. 287. Zheutlin H. and Fox C. L. Jr (1950) Sodium and potassium content of human epidermis. Arch. Dermatol. Syph. 61, 397. Paper

accepted

Programme Further Wachtel Arizona

is available

information

1986.

BURN ASSOCIATION

The nineteenth annual meeting of the American will be held at the Washington Sheraton Hotel, USA on 29 April to 2 May 1987. Accommodation

9 June

at the Washington

will be available

from

Burn Association Washington DC, Sheraton 1 December

Hotel. 1986.

details available from the ABA Secretary Dr T. L. MD, 1130 East McDowell Road, Suite B2, Phoenix, 85006, USA. Telephone 602-239-2391.